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Cardinet, Jean; And Others – Journal of Educational Measurement, 1976
When research focuses on the conditions of measurement, the dimensions of the measurement design should be transposed to differentiate conditions while generalizing over persons. To clarify this transposition, the notions of face of differentiation and face of generalization are introduced as complementary aspects of the design. An example is…
Descriptors: Generalization, Mathematical Models, Research Design, Statistical Analysis
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Takane, Yoshio; Carroll, J. Douglas – Psychometrika, 1981
A maximum likelihood procedure is developed for multidimensional scaling where similarity or dissimilarity measures are taken by such ranking procedures as the method of conditional rank orders or the method of triadic combinations. An example is given. (Author/JKS)
Descriptors: Mathematical Models, Maximum Likelihood Statistics, Multidimensional Scaling
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Hubert, L. J.; Golledge, R. G. – Psychometrika, 1981
A recursive dynamic programing strategy for reorganizing the rows and columns of square proximity matrices is discussed. The strategy is used when the objective function measuring the adequacy of the reorganization has a fairly simple additive structure. (Author/JKS)
Descriptors: Computer Programs, Mathematical Models, Matrices, Statistical Analysis
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Vegelius, Jan – Educational and Psychological Measurement, 1982
The possibility of using a Q-analysis also for nominal data is discussed, using the J-index as a measure of similarity between persons. An example is given when ten persons sorted 16 playing cards into as many groups as they wished. A Q-analysis of these data gave a natural two-dimensional structure. (Author/BW)
Descriptors: Correlation, Factor Analysis, Mathematical Models, Statistical Analysis
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Rosenthal, Robert; Rubin, Donald B. – Journal of Educational Psychology, 1982
The binomial effect size display (BESD) displays the change in success rate attributable to a treatment procedure. It is readily understandable, applicable in varied contexts, and conveniently computed. (Author/GK)
Descriptors: Mathematical Models, Research Methodology, Statistical Significance, Success
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Lastovicka, John L. – Psychometrika, 1981
A model for four-mode component analysis is developed and presented. The developed model, which is an extension of Tucker's three-mode factor analytic model, allows for the simultaneous analysis of all modes of a four-mode data matrix and the consideration of relationships among the modes. (Author/JKS)
Descriptors: Advertising, Data Analysis, Factor Analysis, Mathematical Models
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Mulaik, Stanley A. – Psychometrika, 1981
It is proved for the common factor model that, under certain conditions maintaining the distinctiveness of each factor, a given factor will be determinate if there exists an unlimited number of variables in the model, each having an absolute correlation with the factor greater than some arbitrarily small quantity. (Author/JKS)
Descriptors: Data Analysis, Factor Analysis, Mathematical Models, Statistics
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Wolfle, Lee M. – American Educational Research Journal, 1980
Path analysis is defined for explicitly formulating theory, and for attaching quantitative estimates to causal effects thought to exist on a priori grounds. The four basic kinds of path models are illustrated: (1) recursive; (2) block; (3) block-recursive and (4) nonrecursive. (Author/GDC)
Descriptors: Etiology, Mathematical Models, Path Analysis, Research Design
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Hemker, Bas T.; Sijtsma, Klaas; Molenaar, Ivo W.; Junker, Brian W. – Psychometrika, 1997
Stochastic ordering properties are investigated for a broad class of item response theory (IRT) models for which the monotone likelihood ratio does not hold. A taxonomy is given for nonparametric and parametric models for polytomous models based on the hierarchical relationship between the models. (SLD)
Descriptors: Item Response Theory, Mathematical Models, Nonparametric Statistics
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MacCallum, Robert C.; Hong, Sehee – Multivariate Behavioral Research, 1997
Procedures are presented for conducting power analyses of tests of overall fit of covariance structure models when null and alternative levels of model fit are specified in terms of values of the GFI or AGFI fit indexes. Reasons the root mean square error of approximation fit index may be preferable are discussed. (SLD)
Descriptors: Goodness of Fit, Mathematical Models, Power (Statistics)
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Gentner, Dedre; Markman, Arthur B. – American Psychologist, 1997
It is suggested that both similarity and analogy involve a process of structural alignment and mapping. The structure mapping process is described as it has been worked out for analogy, and this view is then extended to similarity and used to generate new predictions. (SLD)
Descriptors: Analogy, Learning, Mathematical Models, Prediction
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Burrell, Quentin L. – Journal of the American Society for Information Science and Technology, 2003
Shows how the ideas propounded in the notion of Type/Token-Taken (T/TT) informetrics relate to ones that are already well known in informetrics and resolves some of the specific problems posed. (MES)
Descriptors: Information Science, Mathematical Applications, Mathematical Models, Problems
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Thompson, Bruce – Educational and Psychological Measurement, 1997
A general linear model framework is used to suggest that structure coefficients ought to be interpreted in structural equation modeling confirmatory factor analysis (CFA) studies in which factors are correlated. Two heuristic data sets make the discussion concrete, and two additional studies illustrate the benefits of CFA structure coefficients.…
Descriptors: Factor Analysis, Mathematical Models, Structural Equation Models
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Otsu, Tatsuo; Saito, Takayuki – Psychometrika, 1990
A revision of the initialization strategy is suggested for OSMOD, a method of nonlinear principal component analysis for multivariate nominal and/or ordinal data. The revision is effective in diminishing the possibility of obtaining locally optimal solutions with categorical data provided by the original version of OSMOD. (SLD)
Descriptors: Computer Software Development, Mathematical Models, Multivariate Analysis
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Kaplan, David – Multivariate Behavioral Research, 1989
Model modification problems in covariance structure analysis are examined. The Modification Index, suggesting modifications based on a test statistic's largest drop in overall value, and the Expected Parameter Change, suggesting modifications based on the removal of large specification errors, are applied to two specifications of the Wisconsin…
Descriptors: Mathematical Models, Statistical Analysis, Theory Practice Relationship
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